We show that the core of each strongly size monotonic hedonic game is not empty and is externally stable. This is in … sharp contrast to other sufficient conditions for core non-emptiness which do not even guarantee the existence of a stable … set in such games. -- Core ; Hedonic Games ; Monotonicity ; Stable Sets …

either core stability or strict core stability is under consideration, the existence problem of a stable coalition structure …

-emptiness of the strong core and the second domain restriction ensures non-emptiness of the weak core of the corresponding hedonic … games. Moreover, an element of the strong core under friends appreciation can be found in polynomial time, while finding an … element of the weak core under enemies aversion is NP-hard. We examine also the relationship between our domain restrictions …